Works for me. (And yes, New Who companions are mostly *very* tied to their specific plots. Clara's kind of useable anywhere, but she's also kind of vague. Martha and Jack are the only ones who are really flexible, full characters.)
So yes, the GM was... a bit surprised... by our char gen. We hadn't conferred enough, and three characters were *individually* reasonable, but pushing it in aggregate.
Our 4-person UNIT squad has an Ood, a teleporting blue centaur-like life form (doing his anthropology postdoc), and a strange coral-like thing. And one hapless Lt. trying to stay in charge...